Molecular interpretation of nonclassical gas dynamics of dense vapors under the van der Waals model

Abstract

The van der Waals polytropic gas model is used to investigate the role of attractive and repulsive intermolecular forces and the influence of molecular complexity on the possible nonclassical gas dynamic behavior of vapors near the liquid-vapor saturation curve. The decrease of the sound speed upon isothermal compression is due to the well-known action of the van der Waals attractive forces and this effect is shown here to be comparatively larger for more complex molecules with a large number of active vibrational modes; for these fluids isentropic flows are in fact almost isothermal. Contributions to the speed of sound resulting from intermolecular forces and the role of molecular complexity are analyzed in details for both isothermal and isentropic transformations. Results of the exact solution to the problem of a finite pressure perturbation traveling in a still fluid are presented in three exemplary cases: ideal gas, dense gas and nonclassical gas behavior. A classification scheme of fluids based on the possibility of exhibiting different gas dynamic behaviors is also proposed.

The influence of molecular complexity on expanding flows of ideal and dense gases

“…, and ẽ = e / ͑P c v c ͒ in which the parameters M, a, and b are no longer present and the only substance-specific quantity is the molecular complexity N. Therefore, the fundamental derivative of a PVdW gas is a decreasing function of the molecular complexity N and its value depends also on the reduced thermodynamic state, e.g., ͑T , ṽ͒, as follows: 15 PVdW: ⌫͑T ,ṽ͒ =…”

“…14 The above can be appreciated already in the case of an ideal polytropic gas, for which molecular complexity can be conveniently defined as the number N of active degrees of freedom of the molecule. 15 In the temperature range of interest here, these are the translational, rotational, and vibrational degrees of freedom. Both the translational and the rotational modes are assumed to be fully excited, whereas the activation of the vibrational ones occurs only at temperatures higher than the vibrational temperature associated with each mode, hence, N = N͑T͒.…”

“…In this respect, the following classification was proposed in Ref. 15. Fluids with ⌫Ͼ1 everywhere ͓͑‫ץ‬c / ‫ץ‬v͒ s Ͻ 0͔ in the vapor thermodynamic region are classified as low molecular complexity ͑LMC͒ fluids.…”

“…Fluids with ⌫Ͼ1 everywhere ͓͑‫ץ‬c / ‫ץ‬v͒ s Ͻ 0͔ in the vapor thermodynamic region are classified as low molecular complexity ͑LMC͒ fluids. 15,16 For LMC fluids, which are made of simple molecules, real-gas effects are limited to quantitative deviations with respect to ideal-gas fluid dynamic behavior, 24 an exception being the temperature increase due to the Joule-Thompson isenthalpic expansion above a fluid's inversion temperature. Similarly, fluids with 0 Ͻ⌫Ͻ1 in a finite thermodynamic region are termed high molecular complexity ͑HMC͒ fluids since ͑‫ץ‬c / ‫ץ‬v͒ s Ͼ 0.…”

“…In Ref. 15, the authors derived, by means of the physically based Van der Waals equation of state ͑EoSs͒, the relation between the molecular complexity-defined as the capacity of the fluid molecules to store energy into the internal vibrational modes-and the derivative of the sound speed along isentropes, whose value influences real-gas behavior.…”